Measurement by atomic interferometry with multiple species of atoms

ABSTRACT

Disclosed is a method for measuring an external parameter by atomic interferometry, using two sets of atoms that belong to different species. Two measurements are taken simultaneously at the same location, but independently from one another, in order to obtain two measurement results. One of these measurement results removes an indeterminacy among several possible values of the external parameter, by taking into account only the other measurement result. A method of this kind can be used to measure a coordinate of a gravitational field or a coordinate of an acceleration of the atoms.

The present invention relates to a method of measurement by atomicinterferometry, as well as apparatus for implementing this method.

Measurement of an inertial quantity by atomic interferometry is known.The inertial quantity can be a gravitational field coordinate or acoordinate of an acceleration that atoms used for the measurement aresubjected to.

In order to carry out such a measurement, a set of atoms is cooled to atemperature of a few microkelvins, and then subjected to a sequence ofinteractions with photons in order to form atomic interference. A phaseshift that appeared in the resulting matter-wave function for the set ofatoms during formation of the atomic interference is then measured. In aknown manner, when the set of atoms is subject to an acceleration duringthe formation of the interference, the phase shift is ΔΦ=k·a×T²+ΔΦ_(op),where k is the wave vector that corresponds to the momentum received ortransferred by one of the atoms during each interaction between theatoms and the photons, a is the vector of the acceleration that theatoms are subjected to, · denotes the scalar product operation betweenthe vectors k and a, T is a base time that separates successive laserpulses in the sequence of interactions between the atoms and the photonsthat forms the interference, and ΔΦ_(op) is a constant phase shift thatdepends on the manner of producing the interference conditions.

Actually, the measurement result, denoted P, is not the phase shift ΔΦ,directly, but a value that depends on this phase shift via a periodicfunction, according to the formula P=P₀·[1−C×cos(ΔΦ)], where P₀ and Care two non-zero numbers. Owing to the periodicity of the functionP(ΔΦ), several different values for the acceleration component a that isparallel to the wave vector k, are generally compatible with eachmeasurement result P. This results in an indetermination as to which ofthese values correspond to the actual acceleration. More precisely, thevalues of the acceleration component a that corresponds to the samemeasurement result P are:

a _(n)=[Arc cos(1/C−P/(C×P ₀))−ΔΦ_(op) +n×2Π]/(k×T ²) and

a _(n)*=[−Arc cos(1/C−P/(C×P ₀))−ΔΦ_(op) +n×2Π]/(k×T ²)

where k is the modulus of the wave vector k, n is any natural integer,and Arc cos denotes the inverse of the cosinus function. In practice,the value of the acceleration component a is expected to be within aninterval, called an exploration interval, that is known beforehand, butthe length of this interval is greater than Π/(k×T²). Theindetermination between several values a_(n) and/or a_(n)* is thereforereal.

In order to resolve—or eliminate—such an indetermination, it is known tojoin an inertial sensor to the apparatus for measurement by atomicinterferometry, the measurement principle of which is different. Thissensor provides a measurement result for the acceleration component athat is not very precise, but which is sufficient for eliminating theindetermination between the multiple values that are provided by theapparatus for measurement by atomic interferometry. Now these valuesobtained by atomic interferometry each have a high accuracy, so that thecombination of the two apparatuses finally produces a result value thatis single and accurate for the acceleration component.

But the addition of the inertial sensor that does not operate by atomicinterferometry presents numerous drawbacks. Indeed, this inertial sensoris bulky, can be heavy, is capable of generating vibrations, andincreases the cost price of the whole measurement device. In addition,the measurements that are carried out with the atomic interferometryapparatus and with the inertial sensor respectively cannot exactlyrelate to one and same location in space when they are carried outsimultaneously, as the apparatus and the sensor are materially distinct,and therefore separated even if they are close to one another.

Moreover, producing atomic interferences with two sets of atoms ofdifferent species, at one and same location and at one and same timepoint, is known, in particular from the article entitled “SimultaneousDual-Species Matter-Wave Accelerometer”, by A. Bonnin, N. Zahzam, Y.Bidel and A. Bresson, Phys. Rev. A 88, 043615 (2013). Each set of atomsthen provides a measurement result independently of the other set ofatoms. The overall accuracy which results therefrom for eachacceleration value thus determined by double-measurement is improved,but the indetermination between several possible values that has beenshown above remains.

Finally, the article entitled “Simultaneous measurement of gravityacceleration and gravity gradient with an atom interferometer”, by F.Sorrentino et al., Appl. Phys. Lett. 101, 114106 (2012), describes anatomic interference gradiometer. With the type of apparatus in thisdocument, two measurements are performed simultaneously using two setsof atoms of one and same species, but located in two measurementlocations that are remote from one another.

Starting from this situation, a purpose of the present inventionconsists in eliminating such an indetermination between several possiblevalues for a parameter that is determined from measurements carried outby atomic interferometry, when these multiple values are all compatiblewith the measurement results.

An additional purpose of the invention is eliminating theindetermination without having to resort to a supplementary inertialsensor, in addition to the apparatus for measurement by atomicinterferometry.

To achieve this, a first aspect of the invention proposes a method ofmeasurement by atomic interferometry in which each session ofmeasurements is executed with at least two sets of atoms, each of whichis subjected to conditions of formation of an atomic interference. Theatoms of each set of atoms are of a species that is dedicated to thisset of atoms and is different from the species of atoms of each otherset of atoms.

For each session of measurements, the conditions of formation of anatomic interference are produced for each set of atoms throughout avolume that is associated with this set of atoms and that contains atleast one point in common with the volume associated with each other setof atoms. In other words, the atomic interferences are produced in oneand same location for all the sets of atoms, so that the measurementresults that are obtained for the different sets of atoms all relate tothis same location.

Moreover, the conditions of formation of the atomic interference areproduced for each set of atoms between a start time point and an endtime point respectively before and after an intermediate time point thatis common to all the sets of atoms. In other words, the atomicinterferences are produced simultaneously for all the sets of atoms, sothat the measurement results that are obtained for the different sets ofatoms all relate to the intermediate time point.

A measurement result is then obtained in each session of measurementsindependently for each set of atoms, each measurement result varyingaccording to a first function of a phase shift that appeared for the setof atoms during the formation of the atomic interference, and this phaseshift itself being a second function of an external parameter a value ofwhich is sought. Under these conditions, the first function isalternately increasing and decreasing for at least a first of the setsof atoms so that one and same measurement result that is obtained forthis first set of atoms corresponds to several possible values of theexternal parameter within a non-zero exploration interval.Simultaneously, the second function has, for at least one other of thesets of atoms different from the first set of atoms, a derivative withrespect to the value of the external parameter, that depends on at leastone factor selected from a base time for a sequence of interactionsbetween the atoms and photons, and a number of photons involved in amultiphoton interaction, the sequence of interactions or the multiphotoninteraction being implemented in order to form the atomic interferenceof the other set of atoms.

According to the invention, a value of the factor is selected in orderto carry out a session of measurements, so that the measurement resultthat is obtained for the other set of atoms corresponds to a singlevalue of the external parameter within the exploration interval, so thatan indetermination between several values of the external parameter thatexists from the measurement result obtained for the first set of atoms,is eliminated by correlation with the measurement result obtained forthe other set of atoms.

Thus, the invention eliminates the indetermination of the priormeasurement apparatus, without requiring an inertial sensor other thanthe multiple atomic interferometry system.

The first function may have the expression P=P₀·[1−C×cos(ΔΦ(a))] atleast for the first set of atoms, where P denotes the measurementresult, a denotes the external parameter the value of which is sought,ΔΦ(a) is the phase shift and P₀ and C are two non-zero numbers.

The second function may be of the affine function type, at least for theso-called other set of atoms. In this case, a slope coefficient of thisaffine function may be equal to k×T², where T is the base time for thecorresponding sequence of interactions between the atoms and thephotons, and k is a modulus of a momentum received or transferred by oneof the atoms during each interaction between the atoms and the photons,divided by h/(2Π), where h is Planck's constant.

Moreover, a derivative of the measurement result that is obtained duringa session of measurements for the first set of atoms, with respect tothe value of the external parameter, may be greater than the derivativeof the measurement result that is obtained during the same session ofmeasurements for the other set of atoms, also with respect to the valueof the external parameter, in absolute values. Thus, the first set ofatoms provides a better accuracy in the value that is determinedunequivocally thanks to the other set of atoms, for the externalparameter at the end of the session of measurements.

In various embodiments of the invention, two of the species of atoms,which are dedicated to different sets of atoms used in one and samesession of measurements, may be the rubidium isotopes 85 and 87.Alternatively, they can be respective isotopes of rubidium and caesium,or of rubidium and potassium.

In general, the external parameter may be a coordinate of agravitational field, or a coordinate of an acceleration that the atomsare subjected to.

A second aspect of the invention proposes an apparatus for measurementby atomic interferometry that comprises:

-   -   a source of atoms suitable for producing at least two sets of        atoms, with the atoms of each set of atoms that are of a species        dedicated to this set of atoms and different from the species of        atoms of each other set of atoms;    -   means suitable for producing conditions of atomic interference        for each set of atoms, in such a way that these conditions are        produced for each set of atoms throughout a volume that is        associated with the set of atoms and that contains at least one        point in common with the volume associated with each other set        of atoms, and are produced between a start time point and an end        time point respectively before and after an intermediate time        point that is common to all the sets of atoms, so as to        constitute a session of measurements;    -   a detection device, which is arranged to provide measurement        results respectively and independently for all the sets of atoms        of each session of measurements; and    -   an analysis unit, which is suitable for calculating at least one        value of an external parameter from each measurement result.

According to the invention, the apparatus is suitable for implementing amethod that complies with the first aspect of the invention as describedabove, including its variants and its improvements.

Advantageously, for each session of measurements, the conditions ofatomic interferences can be produced for all the sets of atoms using asingle laser assembly, which is common to these sets of atoms.

Such an apparatus may in particular form an accelerometer, a gravimeteror a gyrometer.

Other particular features and advantages of the present invention willbecome apparent from the following description of non-limitativeembodiment examples, with reference to the attached drawings, in which:

FIG. 1 is a general diagram of an apparatus for measurement by atomicinterferometry according to the present invention;

FIG. 2 shows steps of a session of measurements carried out using theapparatus according to FIG. 1;

FIG. 3 shows a particular sequence of interactions for creating atomicinterference, which can be used for implementing the invention; and

FIG. 4 shows a removal of indetermination obtained by applying theinvention.

For sake of clarity, the dimensions of the elements that are shown inthese figures do not correspond to real dimensions or to proportions ofreal dimensions. Moreover, identical references that are indicated indifferent figures denote elements that are identical or that haveidentical functions.

As shown in FIGS. 1 and 2, an apparatus according to the inventioncomprises a source of atoms 100 that is used for producing two sets ofcold atoms 11 and 12, corresponding to step 1 in FIG. 2. Preferably, theatoms of set 11 can be ⁸⁵Rb atoms, and those of set 12 can be ⁸⁷Rbatoms. The source 100 has the function of trapping the atoms of each set11, 12 and cooling them to a specified temperature. It can have one ofthe structures known to a person skilled in the art, such as amagneto-optical trap. Such a trap comprises a pair of coils (not shown)in anti-Helmholtz configuration, which are supplied with electriccurrent during a first phase of operation of the trap in order to createa magnetic field gradient at the location in which each set of atoms isheld. Three pairs of laser beams cross at this location, propagating inopposite directions for two beams of one and the same pair. Thus, beamsF₁ and F₂ propagate in opposite directions along the z axis, beams F₃and F₄ along the x axis and beams F₅ and F₆ along the y axis. Differentmethods of forming beams F₁-F₆, in particular using reflecting mirrorssuch as mirror 101 in order to reduce the number of laser sources thatare required, are so well known that it is not necessary to repeat them.In a second phase of operation of the magneto-optical trap, the magneticfield gradient is suppressed and the radiation frequencies of the laserbeams are detuned in order to obtain the sets of cold atoms 11 and 12,called molasses.

Actually, the source 100 may comprise two injectors of atoms, of ⁸⁵Rband of ⁸⁷Rb respectively, and the magneto-optical trap is controlled inorder to produce two entangled trapping structures, that are intendedfor the ⁸⁵Rb atoms and the ⁸⁷Rb atoms respectively. The source 100 isadjusted so that the two sets 11 and 12 are available at the same timeand in the same location, for each to be subjected to a sequence ofinteractions with photons independently of the other set of atoms.

The sequences of interactions with the photons are then producedsimultaneously for the two sets of atoms 11 and 12, corresponding tosteps 2 ₁ and 2 ₂, in order to produce atomic interference for each ofthese sets independently of the other set. Each sequence may comprise aseries of laser pulses in order to cause stimulated transitions betweentwo states of the atoms of set 11 or 12 to which the sequence isdedicated. Several sequences of pulses can be used alternately,including that which is usually called “Mach-Zehnder” and is describedin the article entitled “Atomic interferometry using stimulated Ramantransitions”, by M. Kasevich et al., Phys. Rev. Lett. 67, pp. 181-184(1991) and which is repeated now:

-   -   a first pulse, called π/2 pulse and having a splitting function        for the wave function of the initial set of atoms, in order to        produce two atomic wave packets;    -   a second pulse, called π and having an atomic mirror function        for each atomic wave packet; and then    -   a third pulse, again π/2 and having a function of recombination        of the atomic wave packets.

This sequence of interactions is shown in FIG. 3, in which t denotestime, and A, B, C and D denote the interactions that a part of the setof atoms in question is subjected to each time. k denotes the moduli ofthe wave vectors k₁₁ and k₁₂ alternately, which will be defined belowfor the sets of atoms 11 or 12 respectively, and similarly for T, whichdenotes the base times T₁₁ and T₁₂ alternately.

In particular, the apparatus configuration that is described in thearticle “A cold atom pyramidal gravimeter with a single laser beam”, byQ. Bodart et al., Appl. Phys. Lett. 96, 134101 (2010), may be adopted.The magneto-optical trap and the means for producing the conditions ofatomic interference are produced using a single laser source assembly,comprising the laser source 102 and the control unit 103. Such anapparatus configuration is simple, economical and very compact.Moreover, the same laser source assembly can be used for both sets ofatoms 11 and 12, as described in the article entitled “SimultaneousDual-Species Matter-Wave Accelerometer”, by A. Bonnin, N. Zahzam, Y.Bidel and A. Bresson, Phys. Rev. A 88, 043615 (2013), so that it has thefollowing four functions:

-   -   trapping and cooling the atoms of set 11;    -   trapping and cooling the atoms of set 12;    -   producing the pulses for creating the atomic wave interferences        for the set of atoms 11; and    -   producing the pulses for creating the atomic wave interferences        for the set of atoms 12.

Each interferometry measurement then proceeds by detection of theproportion of the atoms of the corresponding set that are in a specifiedstate, for example one of two fundamental hyperfine states. Severaldifferent techniques are known to a person skilled in the art forcarrying out such a detection. For example, it may be a measurement oflight absorption, with pulses of radiation the wavelength of which isselected in order to cause absorption from just one of the hyperfineatomic states. Such detections are carried out independently for the twosets of atoms 11 and 12, according to steps 3 ₁ and 3 ₂ in FIG. 2.Suitable detection devices are also assumed to be known, and are notshown in FIG. 1 for the sake of clarity.

A first measurement result, denoted P₁₁, is thus obtained for the set ofatoms 11, and a second measurement result, denoted P₁₂, is also obtainedfor the set of atoms 12. The set of steps formed by the production ofthe two sets of atoms 11 and 12 (step 1), the production of thesimultaneous sequences of interactions with photons, for the two sets ofatoms respectively (steps 2 ₁ and 2 ₂), and the two detections of theproportions of atoms that are finally in a specified state for obtainingthe measurement results P₁₁ and P₁₂ (steps 3 ₁ and 3 ₂), constitute asession of measurements. Such a session is characterized by thesimultaneity of the sequences of interactions that produce the atomicinterferences, and the co-localization of the sets of atoms during thesesequences, whereas the atoms of the two sets are of different species.

Under these conditions, the measurement result P₁₁ is linked tocomponent a along the z axis of the acceleration a that the atoms of set11 undergo, by the following two relationships:

P ₁₁ =P ₀·[1−C×cos(ΔΦ₁₁(a))]

and ΔΦ₁₁(a)=k ₁₁ ×T ₁₁ ² ×a+ΔΦ _(op)

where P₀ and C are two known non-zero numbers,ΔΦ₁₁(a) is the phase shift undergone by the atoms of set 11 duringformation of the atomic interference that is intended for them,k₁₁ is the modulus of the wave vector that corresponds to a momentumreceived or transferred by one of the atoms of the set 11 during eachinteraction between these atoms and the photons,T₁₁ is the base time that separates the successive laser pulses in thesequence of interactions between the atoms of the set 11 and thephotons, andΔΦ_(op) is a constant phase shift that depends on the manner ofproducing the interference conditions for the set of atoms 11.

In the same way, for the atoms of set 12, the measurement result P₁₂ islinked to the same value of component a along the z axis of theacceleration a by the following two other relationships:

P ₁₂ =P ₀′·[1−C′×cos(ΔΦ₁₂(a))]

and ΔΦ₁₂(a)=k ₁₂ ×T ₁₂ ² ×a+ΔΦ _(op)′

where P₀′ and C′ are two known non-zero numbers, which may or may not bedifferent from P₀ and CΔΦ₁₂(a) is the phase shift undergone by the atoms of the set 12 duringformation of the atomic interference that is intended for them,k₁₂ is the modulus of the wave vector that corresponds to a momentumreceived or transferred by one of the atoms of the set 12 during eachinteraction between these atoms and the photons,T₁₂ is the base time which separates the successive laser pulses in thesequence of interactions between the atoms of the set 12 and thephotons, andΔΦ_(op)′ is a constant phase shift that depends on the manner ofproducing the interference conditions for the set of atoms 12, beingable to be different from ΔΦ_(op).

In connection with the terms that have been used in the general part ofthe present description:

-   -   the set of atoms 11 has been called first set of atoms,    -   P₁₁ as a function of ΔΦ₁₁, has been called first function,        effective for the first set of atoms,    -   ΔΦ₁₁ as a function of a, has been called second function,        effective for the first set of atoms,    -   k₁₁×T₁₁ ² is the slope coefficient of the function ΔΦ₁₁(a) which        is of the affine function type    -   the set of atoms 12 has been called other set of atoms,    -   P₁₂ as a function of ΔΦ₁₂, has also been called first function,        but effective for the other set of atoms,    -   ΔΦ₁₂ as a function of a, has also been called second function,        but effective for the other set of atoms,    -   k₁₂×T₁₂ ² is the slope coefficient of the function ΔΦ₁₂(a) which        is also of the affine function type, and    -   a is the external parameter the value of which is sought.

The external parameter a that is measured may be a component of anacceleration, for example due to a translational or rotational movementof a device carrying the apparatus for measurement by atomicinterferometry, or may be a component of a gravitational field in whichthe apparatus is located.

According to the invention, the conditions of formation of the atomicinterference for the set of atoms 12 are selected so that the derivativeof the phase shift ΔΦ₁₂ with respect to the external parameter aeliminates the indetermination that is caused by the periodicity of themeasurement result P₁₁ considered as a function of the same externalparameter a. Practically, starting from the formulae that have beenmentioned above, these conditions of formation are selected so thatk₁₂×T₁₂ ² has a value that is sufficiently different from that ofk₁₁×T₁₁ ². This can be obtained by varying the value of T₁₂ with respectto that of T₁₁, or by varying the value of k₁₂ with respect to that ofk₁₁. Optionally, these two methods can be combined. In other words, thefollowing three alternatives are possible for implementing theinvention:

T ₁₂ ≠T ₁₁ and k ₁₂ =k ₁₁

T ₁₂ =T ₁₁ and k ₁₂ ≠k ₁₁

T ₁₂ ≠T ₁₁ and k ₁₂ ≠k ₁₁ so that k ₁₂ ×T ₁₂ ² ≠k ₁₁ ×T ₁₁ ²

FIG. 4 shows an example of implementation of the invention, in which thevalues of the base time T₁₁, T₁₂ and of the moduli of wave vectors k₁₁and k₁₂ are selected such that k₁₂×T₁₂ ²=( 1/9)×k₁₁×T₁₁ ². Thus, thefunction P₁₂(a) has a period that is nine times larger than that of thefunction P₁₁(a). For the purposes of illustration of FIG. 4, thefollowing values were adopted for the constant numbers: P₀=P₀′=0.5 andC=C′=1.0. In the diagram of FIG. 4, the horizontal axis gives the valuesof the external parameter a in arbitrary units, and the vertical axis,generically denoted P, gives the values of the measurement results P₁₁and P₁₂. The two curves denoted P₁₁(a) and P₁₂(a) correspond to theformulae that were given above. If the interval in which the value of ais sought, called exploration interval and originating for example fromprior knowledge, is smaller than the quarter of the period of thefunction P₁₂(a), then the measurement result P₁₂ makes it possible toeliminate the indetermination that affects the calculation of a startingfrom the single result P₁₁. For example, the values which have beenobtained for the two measurement results P₁₁ and P₁₂ from one and samesession of measurements are those denoted P_(11meas) and P_(12meas). Thevalue of the external parameter a that is deduced from this session ofmeasurements is therefore the single abscissa value in the diagram ofFIG. 4, that solves the two equations P₁₁(a)=P_(11meas) andP₁₂(a)=P_(12meas) simultaneously. This value is shown by an arrow in thediagram, from all the values of a that satisfy individually the equationP₁₁(a)=P_(11meas). All these values are denoted a_(n-2), a_(n-1)*,a_(n-1), a_(n)* . . . according to the formulae concerned that have beengiven in the general part of the present description.

The accuracy in the determination of the value of the external parametera is greater for the measurement that is carried out with the set ofatoms 11, with respect to the accuracy that is provided by themeasurement carried out with the set of atoms 12. In the diagram of FIG.4, this results from the fact that outside the restricted zones aroundthe maxima and the minima of the curve of the function P₁₁(a), thiscurve P₁₁(a) has a slope that is greater than that of the other curveP₁₂(a), in absolute values.

In practice, it is possible that the reports of the two values ofresults P_(11meas) and P_(12meas) which have been obtained for one andthe same session of measurements do not exactly correspond to a singlecommon value for the external parameter a. In this case, the value to beselected for the external parameter a is that from all the values thatsatisfy P₁₁(a)=P_(11meas), that is the closest to the single value of athat satisfies P₁₂(a)=P_(12meas). In other words, the measurement thatis carried out with the set of atoms 12 has the function of eliminatingthe indetermination that results from the measurement carried out withthe set of atoms 11, but this last measurement, carried out from the setof atoms 11, provides the better accuracy for the value of a that isfinally determined.

Analysis of the measurement results P₁₁ and P₁₂ that has just beendescribed for arriving at the single value of the external parameter a(step 4 in FIG. 2), can be executed by an analysis unit (not shown)using a dedicated program.

For example, the base time T₁₁ may be equal to 150 ms (millisecond), andthe base time T₁₂ may be equal to 50 ms. In this case, the moduli of thewave vectors k₁₁ and k₁₂ may be equal.

Moreover, several methods are known for adjusting the moduli of the wavevectors k₁₁ and k₁₂ to different values. The majority of these methodsutilize two laser beams F₁ and F₂ which propagate in opposite directionsin parallel with a common direction (see FIG. 1). Each interactionbetween the radiation of two laser beams and an atom of one of the sets11/12 is of the multiphoton type, and the modulus of the wave vectork_(11/12) that is involved in the formulae mentioned above correspondsto the total momentum p_(tot) that is transferred to the atom duringsuch multiphoton interaction:k_(11/12)=2Πp_(tot)/h=N_(11/12)×k_(laser)=N_(11/12)×2Π/λ_(laser), whereh is Planck's constant, k_(laser) and λ_(laser) are respectively themodulus of the wave vector and the wavelength of the laser radiationconstituting beams F₁ and F₂ (k_(laser)=2Π/λ_(laser)), and N₁₁ and N₁₂denote the numbers of photons that are involved in each multiphotoninteraction, for an atom of set 11 or for an atom of set 12,respectively. The two numbers N₁₁ and N₁₂ can be selected independentlyof one another, from the conditions of formation of atomic interferencefor the concerned set of atoms. Thus, these conditions determine thetypes of multiphoton interactions that are generated and the numberN_(11/12) of photons that are involved in each interaction. For example,each multiphoton interaction may be a diffraction of the atoms byoptical gratings that are formed with beams F₁ and F₂, in Bragg mode orin Bloch oscillation mode with atomic transitions without internalchange of state for the atoms. The article entitled “102 hk Large AreaAtom Interferometers” by S-w. Chiow, T. Kovachy, H-C. Chien and M. A.Kasevich, Phys. Rev. Lett. 107, 130403 (2011), describes implementingmultiphoton Bragg interactions by producing each pulse of radiation ofthe sequence that forms the atomic interference, in the form of a seriesof base subpulses. Alternatively, each multiphoton interaction may be aRaman transition, or a double diffraction caused by an optical grating,i.e. atomic transitions that are accompanied by changes of the internalstate of the atom.

It is understood that the invention can be modified or adapted relativeto the detailed description that has just been given. In particular, thepulse sequence that forms each atomic interference is not necessarily ofthe Mach-Zehnder type, but can be replaced with one of the othersequences known to a person skilled in the art for forming atomicinterference.

Finally, the type of each interaction between atoms and photons that iscaused in each sequence can be varied, provided that the combination ofthe interactions of the sequence once again forms an atomicinterference, and that the wave vectors associated with the totalmomenta that are transferred to the atoms during these interactionssatisfy the present invention.

1. Method of measurement by atomic interferometry, in which each sessionof measurements is executed with at least two sets of atoms (11, 12)each subjected to conditions of formation of an atomic interference, theatoms of each set of atoms (11, 12) being of a species dedicated to saidset of atoms and different from the species of atoms of each other setof atoms, method in which, for each session of measurements, saidconditions are produced for each set of atoms (11, 12) throughout avolume that is associated with said set of atoms and that contains atleast one point in common with the volume associated with each other setof atoms, and are produced between a start time point and an end timepoint respectively before and after an intermediate time point that iscommon to all the sets of atoms, and in which a measurement result (P₁₁,P₁₂) is obtained in each session of measurements independently for eachset of atoms (11, 12), each measurement result varying according to afirst function of a phase shift that appeared for the set of atomsduring the formation of the atomic interference, and said phase shiftitself being a second function of an external parameter (a) a value ofwhich is sought, said first function being alternately increasing anddecreasing for at least a first (11) of the sets of atoms so that ameasurement result (P₁₁) that is obtained for said first set of atomscorresponds to several possible values of the external parameter (a)within a non-zero exploration interval, and said second function having,for at least one other (12) of the sets of atoms different from saidfirst set of atoms (11), a derivative with respect to the value of theexternal parameter (a), that depends on at least one factor selectedfrom a base time (T) for a sequence of interactions between the atomsand photons, and a number of photons involved in a multiphotoninteraction, said sequence of interactions or said multiphotoninteraction being implemented in order to form the atomic interferenceof said other set of atoms, wherein a value of the factor is selected inorder to carry out a session of measurements, so that the measurementresult (P₁₂) that is obtained for said other set of atoms (12)corresponds to a single value of the external parameter (a) within theexploration interval, so that an indetermination between several valuesof the external parameter (a) that exists from the measurement result(P₁₁) obtained for the first set of atoms (11), is eliminated bycorrelation with the measurement result (P₁₂) obtained for said otherset of atoms (12).
 2. Method according to claim 1, wherein the firstfunction has the expression P=P₀·[1−C×cos(ΔΦ(a))] at least for the firstset of atoms (11), where P denotes the measurement result, a denotes theexternal parameter, ΔΦ(a) is the phase shift and P₀ and C are twonon-zero numbers.
 3. Method according to claim 1, wherein the secondfunction is of affine function type at least for said other set of atoms(12).
 4. Method according to claim 3, wherein a slope coefficient of theaffine function is equal to k×T², where T is the base time for thesequence of interactions between the atoms and the photons, and k is amodulus of a momentum received or transferred by one of the atoms duringeach interaction between the atoms and the photons, divided by h/(2Π),where h is Planck's constant.
 5. Method according to claim 1, wherein aderivative of the measurement result (P₁₁) obtained during a session ofmeasurements for the first set of atoms (11), with respect to the valueof the external parameter (a), is greater than the derivative of themeasurement result (P₁₂) obtained during the same session ofmeasurements for said other set of atoms (12), also with respect to thevalue of the external parameter, in absolute values.
 6. Method accordingto claim 1, wherein two of the species of atoms, which are dedicatedrespectively to two of the sets of atoms (11, 12) used in one and samesession of measurements, are the rubidium isotopes 85 and 87, orrespective isotopes of rubidium and caesium, or respective isotopes ofrubidium and potassium.
 7. Method according to claim 1, wherein theexternal parameter (a) is a gravitational field coordinate or acoordinate of an acceleration that atoms are subjected to.
 8. Apparatusfor measurement by atomic interferometry comprising: a source of atoms(100) suitable for producing at least two sets of atoms (11, 12), withthe atoms of each set of atoms that are of a species dedicated to saidset of atoms and different from the species of atoms of each other setof atoms; means (101-103) suitable for producing conditions of atomicinterference for each set of atoms (11, 12), in such a way that saidconditions are produced for each set of atoms throughout a volume thatis associated with said set of atoms and that contains at least onepoint in common with the volume associated with each other set of atoms,and are produced between a start time point and an end time pointrespectively before and after an intermediate time point that is commonto all the sets of atoms, so as to constitute a session of measurements;a detection device, which is arranged to provide measurement results(P₁₁, P₁₂) respectively and independently for all the sets of atoms (11,12) of each session of measurements; and an analysis unit, which issuitable for calculating at least one value of an external parameter (a)from each measurement result (P₁₁, P₁₂), in which each measurementresult (P₁₁, P₁₂) varies according to a first function of a phase shiftthat appeared for the corresponding set of atoms (11, 12) duringformation of the atomic interference, and said phase shift is itself asecond function of the external parameter (a), said first function beingalternately increasing and decreasing for at least a first (11) of thesets of atoms so that one and same measurement result (P₁₁) that isobtained for said first set of atoms corresponds to several possiblevalues of the external parameter (a) within a non-zero explorationinterval, and said second function having, at least for one other (12)of the sets of atoms different from said first set of atoms (11), aderivative with respect to the value of the external parameter (a), thatdepends on at least one factor selected from a base time (T) for asequence of interactions between the atoms and photons, and a number ofphotons involved in a multiphoton interaction, said sequence ofinteractions or said multiphoton interaction being implemented in orderto form the atomic interference of said other set of atoms, theapparatus being characterized in that it is suitable for fixing a valueof the factor so that, for one and same session of measurements, themeasurement result (P₁₂) that is obtained for said other set of atoms(12) corresponds to a single value of the external parameter (a) withinthe exploration interval.
 9. (canceled)
 10. Apparatus according to claim8, in which for each session of measurements, the conditions of atomicinterferences are produced for all the sets of atoms (11, 12) using asingle laser source assembly (102, 103), that is common to said sets ofatoms.
 11. Apparatus according to claim 8, forming an accelerometer, agravimeter or a gyrometer.
 12. Method according to claim 2, wherein thesecond function is of affine function type at least for said other setof atoms (12).
 13. Method according to claim 2, wherein a derivative ofthe measurement result (P₁₁) obtained during a session of measurementsfor the first set of atoms (11), with respect to the value of theexternal parameter (a), is greater than the derivative of themeasurement result (P₁₂) obtained during the same session ofmeasurements for said other set of atoms (12), also with respect to thevalue of the external parameter, in absolute values.
 14. Methodaccording to claim 3, wherein a derivative of the measurement result(P₁₁) obtained during a session of measurements for the first set ofatoms (11), with respect to the value of the external parameter (a), isgreater than the derivative of the measurement result (P₁₂) obtainedduring the same session of measurements for said other set of atoms(12), also with respect to the value of the external parameter, inabsolute values.
 15. Method according to claim 4, wherein a derivativeof the measurement result (P₁₁) obtained during a session ofmeasurements for the first set of atoms (11), with respect to the valueof the external parameter (a), is greater than the derivative of themeasurement result (P₁₂) obtained during the same session ofmeasurements for said other set of atoms (12), also with respect to thevalue of the external parameter, in absolute values.
 16. Methodaccording to claim 2, wherein two of the species of atoms, which arededicated respectively to two of the sets of atoms (11, 12) used in oneand same session of measurements, are the rubidium isotopes 85 and 87,or respective isotopes of rubidium and caesium, or respective isotopesof rubidium and potassium.
 17. Method according to claim 3, wherein twoof the species of atoms, which are dedicated respectively to two of thesets of atoms (11, 12) used in one and same session of measurements, arethe rubidium isotopes 85 and 87, or respective isotopes of rubidium andcaesium, or respective isotopes of rubidium and potassium.
 18. Methodaccording to claim 4, wherein two of the species of atoms, which arededicated respectively to two of the sets of atoms (11, 12) used in oneand same session of measurements, are the rubidium isotopes 85 and 87,or respective isotopes of rubidium and caesium, or respective isotopesof rubidium and potassium.
 19. Method according to claim 5, wherein twoof the species of atoms, which are dedicated respectively to two of thesets of atoms (11, 12) used in one and same session of measurements, arethe rubidium isotopes 85 and 87, or respective isotopes of rubidium andcaesium, or respective isotopes of rubidium and potassium.
 20. Methodaccording to claim 2, wherein the external parameter (a) is agravitational field coordinate or a coordinate of an acceleration thatatoms are subjected to.
 21. Method of measurement by atomicinterferometry, in which each session of measurements is executed withat least two sets of atoms (11, 12) each subjected to conditions offormation of an atomic interference, comprising: providing an apparatusfor measurement by atomic interferometry comprising: a source of atoms(100) suitable for producing at least two sets of atoms (11, 12), withthe atoms of each set of atoms that are of a species dedicated to saidset of atoms and different from the species of atoms of each other setof atoms; means (101-103) suitable for producing conditions of atomicinterference for each set of atoms (11, 12), in such a way that saidconditions are produced for each set of atoms throughout a volume thatis associated with said set of atoms and that contains at least onepoint in common with the volume associated with each other set of atoms,and are produced between a start time point and an end time pointrespectively before and after an intermediate time point that is commonto all the sets of atoms, so as to constitute a session of measurements;a detection device, which is arranged to provide measurement results(P₁₁, P₁₂) respectively and independently for all the sets of atoms (11,12) of each session of measurements; and an analysis unit, which issuitable for calculating at least one value of an external parameter (a)from each measurement result (P₁₁, P₁₂), in which each measurementresult (P₁₁, P₁₂) varies according to a first function of a phase shiftthat appeared for the corresponding set of atoms (11, 12) duringformation of the atomic interference, and said phase shift is itself asecond function of the external parameter (a), said first function beingalternately increasing and decreasing for at least a first (11) of thesets of atoms so that one and same measurement result (P₁₁) that isobtained for said first set of atoms corresponds to several possiblevalues of the external parameter (a) within a non-zero explorationinterval, and said second function having, at least for one other (12)of the sets of atoms different from said first set of atoms (11), aderivative with respect to the value of the external parameter (a), thatdepends on at least one factor selected from a base time (T) for asequence of interactions between the atoms and photons, and a number ofphotons involved in a multiphoton interaction, said sequence ofinteractions or said multiphoton interaction being implemented in orderto form the atomic interference of said other set of atoms, theapparatus being characterized in that it is suitable for fixing a valueof the factor so that, for one and same session of measurements, themeasurement result (P₁₂) that is obtained for said other set of atoms(12) corresponds to a single value of the external parameter (a) withinthe exploration interval; and using the apparatus to perform said methodof measurement, wherein: the atoms of each set of atoms (11, 12) beingof a species dedicated to said set of atoms and different from thespecies of atoms of each other set of atoms, method in which, for eachsession of measurements, said conditions are produced for each set ofatoms (11, 12) throughout a volume that is associated with said set ofatoms and that contains at least one point in common with the volumeassociated with each other set of atoms, and are produced between astart time point and an end time point respectively before and after anintermediate time point that is common to all the sets of atoms, and inwhich a measurement result (P₁₁, P₁₂) is obtained in each session ofmeasurements independently for each set of atoms (11, 12), eachmeasurement result varying according to a first function of a phaseshift that appeared for the set of atoms during the formation of theatomic interference, and said phase shift itself being a second functionof an external parameter (a) a value of which is sought, said firstfunction being alternately increasing and decreasing for at least afirst (11) of the sets of atoms so that a measurement result (P₁₁) thatis obtained for said first set of atoms corresponds to several possiblevalues of the external parameter (a) within a non-zero explorationinterval, and said second function having, for at least one other (12)of the sets of atoms different from said first set of atoms (11), aderivative with respect to the value of the external parameter (a), thatdepends on at least one factor selected from a base time (T) for asequence of interactions between the atoms and photons, and a number ofphotons involved in a multiphoton interaction, said sequence ofinteractions or said multiphoton interaction being implemented in orderto form the atomic interference of said other set of atoms, wherein avalue of the factor is selected in order to carry out a session ofmeasurements, so that the measurement result (P₁₂) that is obtained forsaid other set of atoms (12) corresponds to a single value of theexternal parameter (a) within the exploration interval, so that anindetermination between several values of the external parameter (a)that exists from the measurement result (P₁₁) obtained for the first setof atoms (11), is eliminated by correlation with the measurement result(P₁₂) obtained for said other set of atoms (12).